This invention pertains to orbital mechanics, in general, and in particular, to a method of optimizing the initial inclination and right ascension of the ascending node (RANN) of each of the satellites of a constellation of communication satellites to minimize the amount of onboard propellant required to be carried by the satellites for constellation orbit management while maintaining a selected minimum allowable level of earth coverage during the life of the constellation.
The objective of any constellation of satellites is to provide “good coverage,” defined as continuously maintaining a minimum line-of-sight angle of elevation from selected positions on the surface of the Earth (e.g., ground stations) to at least one of the satellites of the constellation throughout the design life of the constellation. This implies that the constellation is inclined and equally spaced around the Earth such that the right ascension of the ascending node (RAAN) separation between any two satellites of the constellation remains comparable. The satellites share the responsibility for maintaining good coverage by keeping the elevation angle above the minimum allowable at all times during the mission life of the constellation.
In order to share the responsibility for maintaining a sufficient elevation angle, the satellites must be adequately spaced around the Earth via their respective RAANs. The inclined orbit is subject to a variety of perturbative accelerations (e.g. solar and lunar gravity) which induce variations in the orbital parameters, particularly in the inclination itself. The rate of change in RAAN (i.e., nodal regression) of a given satellite is a function of the orbital inclination. Therefore, variations in the inclination will induce variations in nodal regression which, in turn, affect the RAAN separation between any two satellites of a constellation. If the RAAN separation between any two satellites in the constellation varies by a substantial amount, the coverage falls dramatically. The coverage is also extremely sensitive to certain changes in orbital inclination.
Numerous examples of satellite constellations that are adapted to effect good coverage with respect to selected areas of the Earth's surface may be found in the patent literature in, e.g., U.S. Pat. No. 6,714,521 to J. Draim; and, U.S. Pat. Nos. 6,954,613; 6,597,989; 6,122,596; and, 5,931,417, all to D. Castiel. Examples of methods for accurately inserting satellite constellations into common orbital planes are described in, e.g., U.S. Pat. Nos. 6,198,990 and 6,128,575 to C. Croom et al.
Conventionally, the inclination of the respective orbits of the satellites are tightly controlled about some constant mean or target value—often the critical inclination of 63.4° which minimizes the precession of the orbital line of apsides. Small variations in the satellite inclination due to orbital perturbations are controlled with thruster burn maneuvers in order to stay within some small tolerance of the inclination target. With all the satellites in a constellation at effectively the same inclination, there is no need to directly control the satellite RAANs to maintain equitable RAAN separation of the constellation. RAAN separation control is instead effected by making small adjustments to the inclination and thereby achieving the desired nodal regression to maintain equitable RAAN separation. Good coverage is insured by holding the satellite inclinations and the relative RAAN separations effectively constant over the constellation life.
The disadvantage of the prior art solution is that a substantial amount of propellant is used to perform inclination control and thereby maintain good coverage. The large amount of propellant necessary to maintain the constellation limits the mass of the hardware and payload that the satellites can carry, or alternatively, the mission life of the constellation. Thus, if the amount of propellant required to be carried by the satellites can be reduced, the satellites can then carry additional hardware and other payload mass, or alternatively, the design life of the constellation can be increased.